Heptagonal Fuzzy Numbers Research Articles

A New Solution Technique for Fuzzy Transportation Problem Using Novel Ranking Functions on Heptagonal Fuzzy Numbers: A Case Study of Regional Shipment

This study focuses on the fuzzy transportation problem that manifests as a problem of optimization in an uncertain environment. The idea of fuzziness in the objective of transportation cost is based on real-world decision-making difficulties, and the efficiency is demonstrated using the proposed heptagonal fuzzy number. We propose a new ranking technique to de-fuzzify the Linear heptagonal fuzzy number and the proposed $\alpha$-cut based ranking technique has been compared with the existing ranking technique. In addition, we presented an approach for performing multiplication and division for any two heptagonal fuzzy numbers incorporating an example. Furthermore, we have presented a generalized ranking heptagonal fuzzy method (GRHFM) algorithm to solve the heptagonal fuzzy transportation. This article determines the best transportation cost for vegetable shipment from the markets utilizing heptagonal fuzzy numbers, which further compares the feasible solutions obtained using various strategies for fuzzy transportation problems and provides the result from the algorithm. We have demonstrated the effectiveness of our proposed method through a numerical example of an adopted case study. The conclusions section discusses the suggested GRHFM efficiency, outcomes, decision management and future directions based on the existing transportation study.

Optimization of Fuzzy Sequencing Problems with Heptagonal Fuzzy Numbers

Optimization of Fuzzy Sequencing Problems with Heptagonal Fuzzy Numbers

Various defuzzification and ranking techniques for the heptagonal fuzzy number to prioritize the vulnerable countries of stroke disease

The idea of fuzzy numbers is determined according to their uncertainty points, which include interval values, triangular, trapezoidal, and heptagonal fuzzy numbers, etc. This article contains two types of fuzzy numbers: the heptagonal fuzzy number (HpFN) and heptagonal interval-valued fuzzy numbers (HpIVFN). For both the HpFN and HpIVFNs, the new distinct rational perspective and viewpoints are presented. First, the membership function (MF) is generalized to the linear and non-linear for observing the symmetric and asymmetric HpFN and HpIVFN. In light of this, α-cut is constructed for both linear and non-linear MF of HpFN and HpIVFN. The various types of HpIVFNs are classified along with the graphical representation. Then, new defuzzification under HpFN is determined using three methods, namely the centroid method, mean of α-cut method, and removal of area methods, and a comparison is demonstrated. A ranking method is also performed for HpFN. Using the proposed defuzzification approach in the weighted aggregates sum product assessment (WASPAS) method, an analysis is conducted to identify the countries with the highest vulnerability to stroke disease. The results indicated that world Bank upper-middle-income countries is significantly affected by stroke disease. The obtained outcome is validated through comparative and sensitivity analyses.

Fuzzy approach to solve interval-valued transportation problem and comparison of the effectiveness of different fuzzy numbers

In real world, we come across transportation problems, wherein the associated data involves some sort of uncertainty, which at times can be most appropriately represented in the form of interval numbers. Since ordering of intervals involves complexity, hence, we have used fuzzy concept to solve Interval-Valued Transportation Problems (IVTPs). We have proposed new fuzzification methods for conversion of interval number to trapezoidal, pentagonal, hexagonal and heptagonal fuzzy numbers, thereby converting IVTP to Fuzzy Transportation Problem (FTP). Further, we have proposed new ranking functions for conversion of these fuzzy numbers to crisp numbers, which can also be used in other fields of decision making. The crisp-valued transportation problem is then solved using Vogel’s Approximation Method followed by Modified Distribution method. Numerical illustration for the proposed algorithm is given in a later section. The solutions obtained for these examples are used to approximate the solutions for octagonal, nonagonal and decagonal FTPs corresponding to IVTP, using Newton’s Polynomial. On the basis of these solutions, ordering of effectiveness of various types of fuzzy numbers in solving IVTP is done. Lastly, comparison is made between the optimal solutions obtained by various methods. The proposed method can be applied to industrial transportation problems in which the difference between the actual and the proposed demand and supply is quite significant.

Optimal Solution to Transportation Problem with Heptagonal Fuzzy Numbers

In this paper, we have proposed another calculation to track down optimalanswers for the fuzzy transportation problem. Here, positioning strategy is utilized to defuzzify the Heptagonal fuzzy numbers. This article gives procedure that cuts down the optimal arrangement. The mathematical model represents the legitimacy of our proposed technique.

An Interpretation of Non-Preemptive Priority Fuzzy Queuing Model with Asymmetrical Service Rates

This paper presents Non-Preemptive priority fuzzy queuing model with asymmetrical service rates. Arrival rate and service rate are taken to be hexagonal, heptagonal, and octagonal fuzzy numbers. Here an interpretation is given to determine the performance measures by applying a new ranking technique through which the fuzzy values are reduced to the crisp values. This ranking technique has the benefit of being precise and relevant compared to other methods such as alpha-cut method and LR method. The main intention is to evaluate the fuzziness before the performance measures are processed by utilizing the regular queueing hypothesis. Three numerical examples are exhibited to show the validity implementation of the methodology.

On Solutions of Fully Fuzzy Linear Fractional Programming Problems Using Close Interval Approximation for Normalized Heptagonal Fuzzy Numbers

On Solutions of Fully Fuzzy Linear Fractional Programming Problems Using Close Interval Approximation for Normalized Heptagonal Fuzzy Numbers

An Inexact Rough Interval of Normalized Heptagonal Fuzzy Numbers for Solving Vendor Selection Problem

An Inexact Rough Interval of Normalized Heptagonal Fuzzy Numbers for Solving Vendor Selection Problem

Analysis of fuzzy priority queues using heptagonal fuzzy numbers

In this study, a procedure to find the various performance measures in terms of crisp values for non-preemptive priority queuing system, in which the arrival rates and service rate are heptagonal fuzzy numbers has been proposed. DSW algorithm is used to define membership functions of the performance measures of priority queuing system. The α - cut representation of fuzzy sets in a standard interval analysis is used. The validity of the model is checked by a numerical example.

Performance Measure of Fuzzy Simple Queue with Balking and Feedback Customers using Symmetric Heptagonal Fuzzy Numbers

Performance Measure of Fuzzy Simple Queue with Balking and Feedback Customers using Symmetric Heptagonal Fuzzy Numbers

Fuzzy Transportation Problem by Using Triangular, Pentagonal and Heptagonal Fuzzy Numbers With Lagrange's Polynomial to Approximate Fuzzy Cost for Nonagon and Hendecagon

The transportation problem is a main branch of operational research and its main objective is to transport a single uniform good which are initially stored at several origins to different destinations in such a way that the total transportation cost is minimum. In real life applications, available supply and forecast demand, are often fuzzy because some information is incomplete or unavailable. In this article, the authors have converted the crisp transportation problem into the fuzzy transportation problem by using various types of fuzzy numbers such as triangular, pentagonal, and heptagonal fuzzy numbers. This article compares the minimum fuzzy transportation cost obtained from the different method and in the last section, the authors introduce the Lagrange's polynomial to determine the approximate fuzzy transportation cost for the nanogon (n = 9) and hendecagon (n = 11) fuzzy numbers.

Goal programming approach for solving heptagonal fuzzy transportation problem under budgetry constraint

Transportation problem (TP) is a special type of linear programming problem (LPP) where the objective is to minimize the cost of distributing a product from several sources (or origins) to some destinations. This paper addresses a transportation problem in which the costs, supplies, and demands are represented as heptagonal fuzzy numbers. After converting the problem into the corresponding crisp TP using the ranking method, a goal programming (GP) approach is applied for obtaining the optimal solution. The advantage of GP for the decision-maker is easy to explain and implement in real life transportation. The stability set of the first kind corresponding to the optimal solution is determined. A numerical example is given to highlight the solution approach.

Synchronization of Stochastic Modeling with Square Fuzzy Transition Probability Relational Matrix

There are number of fields like agriculture, industry, insurance, tourism and others get affected directly or indirectly by a most common phenomenon known as the Rainfall. Till now we are not able to predict rainfall and it is one of the unsolved problems. This paper aims to synchronize stochastic modeling and square fuzzy transition probability relational matrix and it is obtained from the lexical terms along with the help of fuzzy value which in turn calculated form the lexical value. Fuzzy matrices are necessary in modeling uncertain situations in various fields. Here the lexical values are specially assigned heptagonal fuzzy numbers which in turn converted into fuzzy value to measure relation mappings. Along with this, synchronization is done for stochastic models with transition probability matrix and also with square fuzzy transition probability relation matrix to get a clear picture of the result. In this work, the changes in annual rainfall of Tamil Nadu depending on markov chain models are monitored. Statistical technique like Markov chain is applied at metrological stations in order to predict short term precipitation. The annual rainfall from 1901 to 2000 is derived and the frequency distribution table is formed. The class intervals are denoted as states and the transition probability matrix is formed due to the variations in annual rainfall. The uniform random states are formed by generating random number. The available stochastic climate models presently be adapted to form new climatic conditions if the forthcoming conditions is identified with necessary accuracy. Finally, prediction of rainfall based on two categories such as climatic factors and through states is analyzed in this study.

A new ranking technique on heptagonal fuzzy numbers to solve fuzzy transportation problem

In this work, a general fuzzy transportation problem model is discussed and proposed a new ranking procedure to the heptagonal fuzzy numbers using which convert any fuzzy valued transportation problem to a crisp valued transportation problem which then could be solved using the MODI method. The proposed method serves as an efficient method in ranking heptagonal fuzzy numbers which is illustrated through a numerical example. The purpose of this paper is to give a new ranking index to rank fuzzy numbers effectively. Fuzzy numbers cannot be easily ordered as ordinary real numbers. Several proposals have addressed this problem, each with some drawbacks and limitations. This paper renounces to the idea of finding a universal ordering method for fuzzy numbers.

A new ranking technique on heptagonal fuzzy numbers to solve fuzzy transportation problem

A new ranking technique on heptagonal fuzzy numbers to solve fuzzy transportation problem

Arithmetic Operations on Heptagonal Fuzzy Numbers

Arithmetic Operations on Heptagonal Fuzzy Numbers

A Mathematical Model for Subjective Evaluation of Alternatives in Fuzzy Multi-Criteria Group Decision Making Using COPRAS Method

Multi-criteria group decision-making approaches under fuzzy environment find their attention in the recent works in the area of decision science. In a real-life decision-making situation, decision makers express their opinions often linguistically. Such linguistic expressions are then captured by fuzzy set theory and represented in the present study by heptagonal fuzzy numbers for analytic purpose. Firstly, the concept, the arithmetic operations and a centroid-based ranking method of symmetric heptagonal fuzzy numbers (symHFN) are introduced, and then, some operators are proposed for aggregating the linguistic information. Secondly, the complex proportional assessment (COPRAS) method used for group decision making is extended within the context of the proposed symHFNs to develop an algorithm for fuzzy multi-criteria group decision-making (FMCGDM) method. The proposed method incorporates an efficient computational technique which handles the degree of satisfaction of the decision maker in their judgement. SymHFNs are used to handle the linguistic evaluation and assessment of alternatives by the decision makers. As it records the primary and secondary degree of satisfaction of decision makers’ opinion, symHFN is more suitable and realistic in decision-making problems. Finally, by virtue of the proposed FMCGDM method, fire emergency alternative evaluation is carried out to illustrate the practicality and the effectiveness of the proposed method.

Comparative Study of Arithmetic Nature of Heptagonal Fuzzy Numbers

The uncertainty existing in the available information of many real problems is represented by fuzzy numbers. One type of fuzzy number is Heptagonal fuzzy number and its arithmetic operations can be used to solve many decision making problems involving uncertainty. The existing arithmetic operations do not incorporate all the properties required for the implementation of Heptagonal fuzzy numbers in practical problems. The arithmetic operations of Heptagonal fuzzy numbers based on the extension principle is defined and the arithmetic behavior of Heptagonal fuzzy numbers is observed. In order to improve the efficiency of the arithmetic behavior, a modification in the arithmetic operations is done and a comparison is made with the operations based on the function principle and the extension principle. It is shown through examples, that the proposed modified arithmetic operations are more reasonable, flexible and computationally efficient.

Representation and ranking of fuzzy numbers with heptagonal membership function using value and ambiguity index

In many real life problems, the parameters used to characterize the uncertainty or vagueness or impreciseness in information are either triangular or trapezoidal fuzzy numbers. But it is not always possible to restrict the membership function to either triangular or trapezoidal form. In this paper, a new form of non-normal fuzzy number named as Heptagonal fuzzy number is introduced and its arithmetic operations are defined. Further, an attempt has been made to give a new version of definition for value and ambiguity of non-normal fuzzy numbers and based on this new definition a parametric ranking method is proposed for ordering Heptagonal fuzzy numbers. Finally, an application of Heptagonal fuzzy number in fuzzy assignment problem is given and it is proved that the optimal value obtained using Heptagonal Fuzzy number is more optimal than the solution obtained by using Trapezoidal fuzzy numbers.